Dynamic weighting in simulations of spin systems
(1999)

Tools

"... “Extended Ensemble Monte Carlo ” is a generic term that indicates a set of algorithms which are now popular in a variety of fields in physics and statistical information processing. Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte Carl ..."

“Extended Ensemble Monte Carlo ” is a generic term that indicates a set of algorithms which are now popular in a variety of fields in physics and statistical information processing. Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte Carlo), and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) are typical members of this family. Here we give a cross-disciplinary survey of these algorithms with special emphasis on the great flexibility of the underlying idea. In Sec. 2, we discuss the background of Extended Ensemble Monte Carlo. In Sec. 3, 4 and 5, three types of the algorithms, i.e., Exchange Monte Carlo, Simulated Tempering, Multicanonical Monte Carlo, are introduced. In Sec. 6, we give an introduction to Replica Monte Carlo algorithm by Swendsen and Wang. Strategies for the construction of special-purpose extended ensembles are discussed in Sec. 7. We stress

...classification of 100 samples into 100 clusters. Thus we need to select a model (or mix models) with an appreciate number of parameters. 17 In these works, a “Dynamic Weighting” technique proposed in =-=[94, 111]-=- is used, which does not belong to the class of Extended Ensemble Monte Carlo defined in this paper. 31which deals with simulation-based Bayesian classification of objects to an unknown number of clu...

"... Motivated by the success of genetic algorithms and simulated annealing in hard optimization problems, the authors propose a new Markov chain Monte Carlo (MCMC) algorithm so called an evolutionary Monte Carlo algorithm. This algorithm has incorporated several attractive features of genetic algorithms ..."

Motivated by the success of genetic algorithms and simulated annealing in hard optimization problems, the authors propose a new Markov chain Monte Carlo (MCMC) algorithm so called an evolutionary Monte Carlo algorithm. This algorithm has incorporated several attractive features of genetic algorithms and simulated annealing into the framework of MCMC. It works by simulating a population of Markov chains in parallel, where each chain is attached to a different temperature. The population is updated by mutation (Metropolis update), crossover (partial state swapping) and exchange operators (full state swapping). The algorithm is illustrated through examples of the Cp-based model selection and change-point identification. The numerical results and the extensive comparisons show that evolutionary Monte Carlo is a promising approach for simulation and optimization.

"... This article provides a first theoretical analysis of a new Monte Carlo approach, the dynamic weighting algorithm, proposed recently by Wong and Liang. In dynamic weighting Monte Carlo, one augments the original state space of interest by a weighting factor, which allows the resulting Markov chain t ..."

This article provides a first theoretical analysis of a new Monte Carlo approach, the dynamic weighting algorithm, proposed recently by Wong and Liang. In dynamic weighting Monte Carlo, one augments the original state space of interest by a weighting factor, which allows the resulting Markov chain to move more freely and to escape from local modes. It uses a new invariance principle to guide the construction of transition rules. We analyze the behavior of the weights resulting from such a process and provide detailed recommendations on how to use these weights properly. Our recommendations are supported by a renewal theory-type analysis. Our theoretical investigations are further demonstrated by a simulation study and applications in neural network training and Ising model simulations.

"... Simulated annealing has been one of the most popular stochastic optimization methods used in the VLSI CAD eld in the past two decades. Recently, a new Monte Carlo and optimization method, named dynamic weighting Monte Carlo [WL97], has been introduced and successfully applied to the traveling salesm ..."

Simulated annealing has been one of the most popular stochastic optimization methods used in the VLSI CAD eld in the past two decades. Recently, a new Monte Carlo and optimization method, named dynamic weighting Monte Carlo [WL97], has been introduced and successfully applied to the traveling salesman problem, neural network training [WL97], and spin-glasses simulation [LW99]. In this paper, we have successfully applied dynamic weighting Monte Carlo algorithm to the constrained oorplan design with consideration of both area and wirelength minimization. Our application scenario is the constrained oorplan design for mixed signal MCMs, where we need to place all the analog modules together in groups so that they can share common power and ground planes, which are separate from those used by the digital modules. Our experiments indicate that the dynamic weighting Monte Carlo algorithm is very effective for constrained oorplan optimization. It outperforms the simulated annealing for a real mixed signal MCM design by 19:5 % in wirelength, with slight area improvement. This is the rst work adopting the dynamic weighting Monte Carlo optimization method for solving VLSI CAD problems. We believe that this method has applications to many other VLSI CAD optimization problems. I.

...ization method, named dynamic weighting Monte Carlo [WL97], has been introduced and successfully applied to the traveling salesman problem, neural network training [WL97], and spin-glasses simulation =-=[LW98]-=-. In this paper, we have successfully applied dynamic weighting Monte Carlo algorithm to the constrained floorplan design with consideration of both area and wirelength minimization. Our application s...

"... This article provides a first theoretical analysis on a new Monte Carlo approach, the dynamic weighting, proposed recently by Wong and Liang. In dynamic weighting, one augments the original state space of interest by a weighting factor, which allows the resulting Markov chain to move more freely and ..."

This article provides a first theoretical analysis on a new Monte Carlo approach, the dynamic weighting, proposed recently by Wong and Liang. In dynamic weighting, one augments the original state space of interest by a weighting factor, which allows the resulting Markov chain to move more freely and to escape from local modes. It uses a new invariance principle to guide the construction of transition rules. We analyze the behaviors of the weights resulting from such a process and provide detailed recommendations on how to use these weights properly. Our recommendations are supported by a renewal theory-type analysis. Our theoretical investigations are further demonstrated by a simulation study and applications in the neural network training and the Ising model simulations. Keywords: Gibbs Sampling; Importance Sampling; Ising Model, Metropolis algorithm, Neural Network, Renewal Theory, Simulated Annealing, Simulated Tempering, 1 Jun S. Liu is Assistant Professor, Department of Statisti...

...and Sokal (1989) can be successful for some other models but is not suitable for the Ising model. We now review the results obtained on Ising model simulations by dynamic weighting with R-type moves (=-=Liang and Wong 1998-=-). The simulations were done on lattices of size 32 2 , 64 2 and 128 2 . Similar to simulated tempering, we treat the inverse temperature K as a dynamic variable taking values in a ladder of suitable ...